5.2 Combined Events

• Independent events are affected by each other's outcomes

  False
• Rolling a die and flipping a coin are examples of independent events


  True
• For independent events, the probability of both A and B happening is calculated as P(A) * P(B)
• Independent events have self-contained probabilities, while dependent events have probabilities that change based on previous outcomes
• For dependent events, the AND condition is calculated as P(A AND B) = P(A) * P(B|A)
• For dependent events, the AND condition is calculated as P(A AND B) = P(A) * P(B|A)
• The AND condition for dependent events is calculated as P(A AND B) = P(A) * P(B|A)
• How is the AND condition calculated for dependent events?

  P(A) * P(B|A)
• For independent events, the AND condition is calculated as P(A) * P(B)
• The OR condition formula is P(A OR B) = P(A) + P(B) - P(A AND B)
• For independent events, the AND condition is calculated as P(A) * P(B)
• The AND condition depends on whether events are independent
• What are combined events?

  Two or more events happening
• What is the formula for the probability of either A or B happening (OR condition)?

  P(A) + P(B) - P(A AND B)
• Give an example of dependent events.

  Selecting balls without replacement
• What is the formula for the OR condition for both independent and dependent events?

  P(A) + P(B) - P(A AND B)
• What is the AND condition formula for independent events?

  P(A) * P(B)
• What is the characteristic of dependent events in probability?

  One event affects the other
• Combined events occur when two or more events happen simultaneously or in sequence


  True
• What does P(B|A) represent in probability?

  Probability of B given A
• Match the event type with its example:

  Independent Event ↔️ Flipping a coin twice

  Dependent Event ↔️ Drawing cards without replacement
• The OR condition formula is the same for both independent and dependent events


  True
• For dependent events, the AND probability requires conditional probability


  True
• What is the key difference between independent and dependent events in calculating the OR condition?

  None
• What is the formula for P(A AND B) when events A and B are independent?

  $P(A AND B) =$$P(A) *$$P(B)$
• Combined events occur when two or more events happen simultaneously or in sequence.


  True
• Match the type of event with its characteristic:

  Independent Events ↔️ Probabilities remain constant

  Dependent Events ↔️ Probabilities change
• Independent events have constant probabilities regardless of prior outcomes.


  True
• Steps to calculate "AND" probabilities

  1️⃣ Identify whether events are independent or dependent

  2️⃣ For independent events: P(A AND B) = P(A) * P(B)

  3️⃣ For dependent events: P(A AND B) = P(A) * P(B\|A)
• The formula for the OR probability applies to both independent and dependent
• For independent events, the AND probability is calculated by multiplying the individual probabilities
• If P(A) = 0.4, P(B) = 0.6, and P(A AND B) = 0.2, what is P(A OR B)?

  $0.8$
• In a Venn diagram, the overlapping region represents the AND condition, denoted as P(A AND B).
• The formula for P(A OR B) in a Venn diagram is (Area of A + Area of B) - Area of overlap / Total area.
• Match the type of event with its characteristic:

  Independent Event ↔️ Outcome of one does not affect the other

  Dependent Event ↔️ Outcome of one changes the probability of the other
• The formula for P(A OR B) is the same for both independent and dependent events.


  True
• For dependent events, P(A AND B) is calculated as P(A) * P(B|A).


  True
• The OR condition formula applies to both independent and dependent events.


  True
• P(B|A) represents the probability of event B occurring given that event A has already occurred.


  True
• The formula for the OR condition is P(A OR B) = P(A) + P(B) - P(A AND B).


  True